For applications such as virtual reality and mobile mapping, point clouds are an effective means for representing 3-D environments. The need for compressing such data is rapidly increasing, given the widespread use and precision of these systems. This paper presents a method for compressing organized point clouds. 3-D point cloud data is mapped to a 2-D organizational grid, where each element on the grid is associated with a point in 3-D space and its corresponding attributes. The data on the 2-D grid is hierarchically partitioned, and a Bezier patch is fit to the 3-D coordinates associated with each partition. Residual values are quantized and signaled along with data necessary to reconstruct the patch hierarchy in the decoder. We show how this method can be used to process point clouds captured by a mobile-mapping system, in which laser-scanned point locations are organized and compressed. The performance of the patch-fitting codec exceeds or is comparable to that of an octree-based codec.